3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can be used to reduce complexity. Existing PC sampling algorithms focus on preserving geometry features and often do not scale to handle large PCs. In this work, we develop scalable graph-based sampling algorithms for PC color attributes, assuming the full geometry is available. Our sampling algorithms are optimized for a signal reconstruction method that minimizes the graph Laplacian quadratic form. We first develop a global sampling algorithm that can be applied to PCs with millions of points by exploiting sparsity and sampling rate adaptive parameter selection. Further, we propose a block-based sampling strategy where each block is sampled independently. We show that sampling the corresponding sub-graphs with optimally chosen self-loop weights (node weights) will produce a sampling set that approximates the results of global sampling while reducing complexity by an order of magnitude. Our empirical results on two large PC datasets show that our algorithms outperform the existing fast PC subsampling techniques (uniform and geometry feature preserving random sampling) by 2dB. Our algorithm is up to 50 times faster than existing graph signal sampling algorithms while providing better reconstruction accuracy. Finally, we illustrate the efficacy of PC attribute sampling within a compression scenario, showing that pre-compression sampling of PC attributes can lower the bitrate by 11% while having minimal effect on reconstruction.

翻译：三维点云通常用于表示三维场景。点云可能包含数百万个点，使得后续的下游任务（如压缩和流式传输）计算成本高昂。点云采样（选择点的子集）可用于降低复杂度。现有的点云采样算法侧重于保留几何特征，且通常难以扩展到处理大规模点云。在本工作中，我们假设完整几何信息可用，针对点云颜色属性开发了可扩展的基于图的采样算法。我们的采样算法针对最小化图拉普拉斯二次型的信号重建方法进行了优化。我们首先开发了一种全局采样算法，该算法通过利用稀疏性和采样率自适应参数选择，可应用于包含数百万个点的点云。此外，我们提出了一种基于分块的采样策略，其中每个块独立采样。我们证明，通过最优选择自环权重（节点权重）对相应子图进行采样，将产生近似全局采样结果的采样集，同时将复杂度降低一个数量级。我们在两个大型点云数据集上的实验结果表明，我们的算法比现有的快速点云子采样技术（均匀采样和几何特征保持随机采样）性能提升2dB。在提供更好重建精度的同时，我们的算法比现有图信号采样算法快达50倍。最后，我们在压缩场景中展示了点云属性采样的有效性，表明点云属性的预压缩采样可将比特率降低11%，同时对重建质量影响极小。